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The paradoxes of material implication are a group of true formulae involving material conditionals whose translations into natural language are intuitively false when the conditional is translated as "if ... then ...". A material conditional formula is true unless is true and is false. If natural language conditionals were understood in the same way, that would mean that the sentence "If the Nazis had won World War Two, everybody would be happy" is vacuously true. Given that such problematic consequences follow from a seemingly correct assumption about logic, they are called paradoxes. They demonstrate a mismatch between classical logic and robust intuitions about meaning and reasoning.[1]
^von Fintel, Kai (2011). "Conditionals" (PDF). In von Heusinger, Klaus; Maienborn, Claudia; Portner, Paul (eds.). Semantics: An international handbook of meaning. de Gruyter Mouton. pp. 1515–1538. doi:10.1515/9783110255072.1515. hdl:1721.1/95781. ISBN 978-3-11-018523-2.
and 23 Related for: Paradoxes of material implication information
The paradoxesofmaterialimplication are a group of true formulae involving material conditionals whose translations into natural language are intuitively...
replace materialimplication with other operators such as the strict conditional and the variably strict conditional. Due to the paradoxesofmaterial implication...
strict implication, on the grounds that classical logic grants paradoxesofmaterialimplication such as the principle that a falsehood implies any proposition...
Connexive logic is a class of non-classical logics designed to exclude the paradoxesofmaterialimplication. The characteristic that separates connexive...
product Empty function Paradoxesofmaterialimplication, especially the principle of explosion Presupposition, double question State of affairs (philosophy)...
conditionals may avoid paradoxesofmaterialimplication. The following statement, for example, is not correctly formalized by materialimplication: If Bill Gates...
logical paradoxes and semantic paradoxes, with Russell's paradox belonging to the former category, and the liar paradox and Grelling's paradoxes to the...
of disjunction in alternative questions. Other apparent discrepancies between natural language and classical logic include the paradoxesofmaterial implication...
that materialimplication does not fully capture the meaning of "If A {\displaystyle A} then B {\displaystyle B} " (see the paradoxesofmaterial implication)...
semantics of ⇒ {\displaystyle \Rightarrow } (or of negation) is often rejected by relevantists in their bid to escape the `paradoxesofmaterialimplication',...
logic, and specifically strict implication, on the grounds that classical logic grants paradoxesofmaterialimplication such as the principle that a falsehood...
Siami, Navid; Winter, Ralph A. (1 September 2021). "Jevons' paradox revisited: Implications for climate change". Economics Letters. 206: 109955. doi:10...
liar paradox, it does not rely on self-reference, raising questions about the nature ofparadoxes and infinity. Zeno paradoxes A series ofparadoxes proposed...
principle List ofparadoxes Maxwell's demon No-hair theorem No-hiding theorem Thorne–Hawking–Preskill bet The short form "ínformation paradox" is also used...
Syllabus of a Proposed System of Logic. London: Walton & Malbery. 1860. A Budget ofParadoxes. London: Longmans, Green. 1872. History of Grandi's series...
Karlawish J (December 2021). "The ethical implicationsofparadoxical lucidity in persons with dementia". Journal of the American Geriatrics Society. 69 (12):...
is an activity of passing from sentences to sentences, whereas A → B is simply a formula made with a logical connective, implication in this case. Without...
brief allegorical dialogue on the foundations of logic. The title alludes to one of Zeno's paradoxesof motion, in which Achilles could never overtake...
paradox. Russell named paradoxes after Cesare Burali-Forti and Cantor even though neither of them believed that they had found paradoxes. In 1908, Zermelo...
contrapositives are logically equivalent, we need to understand when materialimplication is true or false. P → Q {\displaystyle P\to Q} This is only false...
of Logical Calculi: Basic Theory of Consequence Operations. Springer. ISBN 978-90-277-2785-5. A paper on 'implication' from math.niu.edu, Implication...
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